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    Cot 210 Degrees

    Sin, Cos, Tan, Cot of an Angle
    Function
    Angle (°)

    What is cot 210°?

    Answer

    cot 210° =
    √3 ≈ 1.7321

    Angle in radians: 210° = 7π/6. The point of the angle is in quadrant III, where cotangent is positive.

    ≈ — rounded to 4 decimal places.

    cot 210° = cot(180° + 30°) = cot 30° = √3

    cot 210° = cos 210° / sin 210° = (−√3/2) / (−1/2) = √3

    Half of an equilateral triangle with side 1: the hypotenuse is 1 and the leg opposite 30° is 1/2.

    cot 30° = (√3/2) / (1/2) = √3

    xyOP

    P(cos 210°, sin 210°) ≈ (−0.8660, −0.5)

    C(cot 210°, 1) ≈ (1.7321, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed).

    All four functions of 210°
    FunctionExact valueDecimal
    sin 210°−1/2−0.5
    cos 210°−√3/2≈ −0.8660
    tan 210°√3/3≈ 0.5774
    cot 210°√3≈ 1.7321

    Reference angle: cot 30° = √3

    See Also

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    https://calculat.io/en/number/trigonometry/cot--210Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--210">Cot 210 Degrees: Cotangent of 210° on the Unit Circle</a>Copy
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    Cot 210 Degrees: Cotangent of 210° on the Unit Circle. cot 210° = √3 ≈ 1.7321. The cotangent is the ratio x/y of the point at 210° on the unit circle; 210° reduces to 30°.
    https://calculat.io/en/number/trigonometry/cot--210/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    195°2 + √3
    198°√(5 + 2√5)
    200°≈ 2.7475
    210°√3
    211°≈ 1.6643
    215°≈ 1.4281
    216°√(25 + 10√5)/5
    Recalculate with different values ↑

    FAQ

    What is cot 210°?

    cot 210° = √3 ≈ 1.7321

    How to remember sin 30°, sin 45° and sin 60°?

    Write them as √1/2, √2/2, √3/2: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2. Cosines are the same numbers in reverse order: cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2; tan = sin / cos and cot = cos / sin. Here: cot 210° = √3 ≈ 1.7321.

    Why does a calculator show −1.8898 for cot 210?

    The calculator is in radian mode (RAD): it takes cot 210 as the cotangent of 210 radians, cot 210 rad ≈ −1.8898. Switch it to degrees (DEG): cot 210° = √3 ≈ 1.7321. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also